Autofrettaged cylindrical vessels and Bauschinger effect: an analytical frame for evaluating residual stress distributions

The paper reports analytical solutions valid for residual stresses in cylindrical pressure vessels subjected to autofrettage. The material behavior is thought of as obeying a generic monotonic sigma-epsilon curve and exhibiting the Bauschinger effect during the unloading phase. Under linear and power-hardening conditions, the solution is given in tin explicit form. The circumstances under which it is possible to apply the superposition principle also in the presence of localized plasticity are clearly identified. When possible, the final stresses can be obtained by using in an appropriate manner the stress expressions related to the loading phase. Finally, the influence on residual stresses, both of the hardening law and of the shape of the unloading sigma-epsilon curve, is discussed.